If you've got the bandwidth and time to wait for a better picture, you can have YouTube automatically load the best possible resolution when you take a video full screen. It's a switch tucked away in your "Video Playback Quality" settings.

You can head right to the setting if you're already logged into YouTube/Google, or head there from the new-ish "Settings" option that appears at the top of the resolution switcher. Check "Always choose HD when switching to fullscreen" on, and YouTube should take care of the rest, at least when you're logged in. Add in keeping videos in full screen when clicking elsewhere, and the web becomes a much nicer theater.